Sensor Fusion Latency & Sampling Rate Alignment Calculator
Calculate the effective fusion latency, least common sampling period, synchronization buffer size, and phase alignment error for multi-sensor fusion systems.
Sensor A
Sensor B
Sensor C (optional)
Fusion Parameters
Formulas Used
Sampling Period: Ti = 1000 / fi (ms)
LCM Alignment Period: Tlcm = LCM(TA, TB, ...) — the smallest window in which all sensors produce an integer number of samples, computed via the Euclidean GCD algorithm.
Fusion Output Rate: ffusion = 1000 / Tlcm (Hz)
Effective Fusion Latency: Leff = max(Li) + Lfusion + Ltransport
Worst-Case Latency: Lworst = Leff + σjitter
Phase Alignment Error: εphase = Tmax / 2 — worst-case temporal misalignment between unsynchronized sensors equals half the longest sampling period.
Nyquist Fusion Bandwidth: BWNyquist = fmin / 2 — the fused output cannot faithfully represent signals above half the slowest sensor's rate.
Buffer Size per Sensor: Ni = ⌈fi × Tlcm / 1000⌉ (samples)
Assumptions & References
- All sensors are assumed to have stable, periodic sampling clocks (no drift beyond the specified jitter).
- LCM is computed on floating-point periods scaled to microsecond precision to handle non-integer rates.
- Effective latency uses the maximum sensor latency because the fusion algorithm must wait for the slowest sensor's data before producing an output.
- Phase alignment error of Tmax/2 is the worst-case bound for unsynchronized sensors; hardware timestamping or PTP/IEEE 1588 can reduce this to sub-millisecond levels.
- Nyquist criterion: Shannon–Nyquist sampling theorem (Nyquist, 1928; Shannon, 1949).
- Buffer sizing assumes a sliding-window approach over one LCM period; real implementations may require additional margin for jitter buffering.
- Fusion algorithm latency (Lfusion) covers Kalman filter, complementary filter, or other fusion computation time and must be measured empirically for the target hardware.
- Reference: Liggins, Hall & Llinas, Handbook of Multisensor Data Fusion, 2nd ed., CRC Press, 2008.